2.1.1 RasterLayer

# Chunk 1
# #1
e <- extent(c("xmin" = 27, "xmax" = 29, "ymin" = -16, "ymax" = -14))  
#
# #2
r <- raster(x = e, res = 0.25, crs = crs(districts))
#
# #3            
set.seed(1)  
values(r) <- sample(1:100, size = ncell(r), replace = TRUE)  # 3
# r[] <- sample(1:100, size = ncell(r), replace = TRUE) 
# r <- setValues(x = r, values = sample(1:100, size = ncell(r), replace = TRUE))

par(mar = c(0, 0, 0, 4))
plot(st_geometry(districts), col = "grey", reset = FALSE)
plot(r, add = TRUE)

We just used several functions from the raster package to create a random raster named r that has a 1/4 degree resolution and covers an area of 2 X 2 degrees in southern Zambia. This particular raster is a temporary one that lives in memory.

Let’s walk through the labelled code. In # 1, we use raster’s extent function to define the boundaries of the raster, and then in # 2 use the raster function to create a raster from the resulting Extent object e, assigning a CRS using the “crs” argument, which in turn uses raster’s crs to extract the crs from districts (#3). crs is similar to sf::st_crs, but outputs a different class of object that can’t be used by raster. The raster function can create a raster from many different types of input objects (passed to argument “x”), per ?raster:

filename (character), Extent, Raster, SpatialPixels, SpatialGrid*, object, ‘image’, matrix, im, or missing. Supported file types are the ‘native’ raster package format and those that can be read via rgdal

Line # 2 creates an empty raster r with no cell values, so in # 3 we assign some randomly selected values into r. Note the method of assignment, using the values function; there are two other lines commented out below # 3 that show different ways of doing the same job.

The plot of r over districts uses the plot method defined for raster* objects. Note that it automatically creates a continuous legend, and also note that raster::plot can work with sf::plot.

Let’s look now at the structure of the object r.

# Chunk 2
r
#> class      : RasterLayer 
#> dimensions : 8, 8, 64  (nrow, ncol, ncell)
#> resolution : 0.25, 0.25  (x, y)
#> extent     : 27, 29, -16, -14  (xmin, xmax, ymin, ymax)
#> crs        : +proj=longlat +datum=WGS84 +no_defs 
#> source     : memory
#> names      : layer 
#> values     : 1, 100  (min, max)
class(r)
#> [1] "RasterLayer"
#> attr(,"package")
#> [1] "raster"
typeof(r)
#> [1] "S4"
slotNames(r)
#>  [1] "file"     "data"     "legend"   "title"    "extent"   "rotated"  "rotation" "ncols"   
#>  [9] "nrows"    "crs"      "history"  "z"
values(r)
#>  [1]  68  39   1  34  87  43  14  82  59  51  97  85  21  54  74   7  73  79  85  37  89  37  34  89
#> [25]  44  79  33  84  35  70  74  42  38  20  28  20  44  87  70  40  44  25  70  39  51  42   6  24
#> [49]  32  14   2  45  18  22  78  65  70  87  70  75  81 100  13  40
# slot(slot(r, "data"), "values")  # identical to values(r)
res(r)
#> [1] 0.25 0.25

r is an S4 object that has fairly different slots compared to sf objects. We are not going to go into all of them, but it is useful to know the @file, @data, @extent, and @crs slots. @file itself holds a number of slots, but you should know the @file@name slot, which contains the file name and path for grids that that are read in from disk (it is empty in the case of r, since it is held in memory). @data contains many slots also, but the main one of interest is the @data@values slot, which can be accessed with the values function directly, or less directly using slot (both approaches are shown above). Interestingly, the resolution information is not stored in any of the slots of r, but rather calculated from the @extent and @ncols and @nrows slots by the res function.

2.1.2 RasterStack and RasterBrick

We have just seen how to create a RasterLayer and learned a bit about the structure of this kind of object, which is two-dimensional. We are now going to learn about three-dimensional rasters, which come in two flavors: RasterStack and RasterBrick. Before we proceed, we first need to create some new data.

# Chunk 3
r2 <- r > 50
r3 <- r
set.seed(1)
values(r3) <- rnorm(n = ncell(r3), mean = 10, sd = 2)
l <- list(r, r2, r3)

We used r to create two new rasters, r2 and r3. r2 was made by using a logical operator (>) to find the locations where r’s values exceed 50, creating a binary raster where 1 indicates the matching pixels, and 0 those that don’t. r3 was made by using r as a template, then overwriting the values with numbers generated randomly from a normal distribution (rnorm). These were then combined into list l.

# Chunk 4
s <- stack(l)
# s <- stack(r, r2, r3)  # also works
names(s) <- c("r", "r2", "r3")
s
#> class      : RasterStack 
#> dimensions : 8, 8, 64, 3  (nrow, ncol, ncell, nlayers)
#> resolution : 0.25, 0.25  (x, y)
#> extent     : 27, 29, -16, -14  (xmin, xmax, ymin, ymax)
#> crs        : +proj=longlat +datum=WGS84 +no_defs 
#> names      :         r,        r2,        r3 
#> min values :    1.0000,    0.0000,    5.5706 
#> max values : 100.00000,   1.00000,  14.80324

b <- brick(s)
b
#> class      : RasterBrick 
#> dimensions : 8, 8, 64, 3  (nrow, ncol, ncell, nlayers)
#> resolution : 0.25, 0.25  (x, y)
#> extent     : 27, 29, -16, -14  (xmin, xmax, ymin, ymax)
#> crs        : +proj=longlat +datum=WGS84 +no_defs 
#> source     : memory
#> names      :         r,        r2,        r3 
#> min values :    1.0000,    0.0000,    5.5706 
#> max values : 100.00000,   1.00000,  14.80324

plot(b, nr = 1)

In the preceding code blocks, we use l to create a RasterStack and RasterBrick. These are very similar things, but have a few key differences. A RasterStack is a series of rasters that have the same extent and resolution, which are “stacked” on top of one another in the order that they are given in the input list. The stacked layers can from any number of files stored in different areas on disk. A RasterBrick does the same thing (stacks RasterLayers on top of one another), but is more restrictive because the layers, if read off disk, must be contained within a single file. This makes the RasterBrick less flexible than the RasterStack, but it has the advantage of faster processing times (according to ?brick).

Applying plot to a stack or brick results in the automatic plotting of each layer into its own sub-window, with coordinates along the plot axes. You can specify numbers of rows and columns in your plotting device using the “nc” and “nr” arguments to raster::plot.

Here’s a more informative (by putting it over a map of Zambia) way of plotting the layers in s (works for b also):

# Chunk 5
par(mfrow = c(1, 3), mar = c(0, 0, 0, 4))
for(i in 1:nlayers(s)) {
  districts %>% st_geometry %>% plot(col = "grey")
  plot(s[[i]], add = TRUE)
}

2.3.1 Vector to raster

We have several vector datasets that come with geospaar which we can rasterize, starting with the district boundaries.

# Chunk 7
# #1
zamr <- raster(x = extent(districts), crs = crs(districts), res = 0.1)
values(zamr) <- 1:ncell(zamr)
#
# #2
districts <- districts %>% mutate(ID = 1:nrow(.))
distsr <- districts %>% rasterize(x = ., y = zamr, field = "ID") %>% print()
#> class      : RasterLayer 
#> dimensions : 98, 117, 11466  (nrow, ncol, ncell)
#> resolution : 0.1, 0.1  (x, y)
#> extent     : 21.99978, 33.69978, -18.02621, -8.226213  (xmin, xmax, ymin, ymax)
#> crs        : +proj=longlat +datum=WGS84 +no_defs 
#> source     : memory
#> names      : layer 
#> values     : 1, 72  (min, max)

par(mar = c(0, 0, 0, 4))
plot(distsr, axes = FALSE, box = FALSE)

In #1, we took an initial step to define a raster (zamr) that has the properties of resolution (0.1 decimal degrees), CRS, and extent that we want our rasterized vector to have. We set the extent of this raster to that of districts, using extent to get the bounding box coordinates (extent retrieves the same parameters as sf::st_bbox, but the output is in a different format).

In #2, we use rasterize to (as the name says) rasterize districts. The “y” argument is where we feed in zamr, the raster object that is the “target” for rasterizing districts. The “field” argument supplies the column names of the values that we want rasterized. In this case, we have to first create an “ID” variable for districts, in order to give an integer for each district name, as the district names (a character variable) cannot be written to the raster. Notice that we have constructed this as a pipeline (with print as the last step, to show the raster metadata). The commented out code below it shows how it can be done with more conventional syntax.

Our plot removes the coordinate-labelled axes and box that otherwise drawn around raster plots by default.

Next we rasterize the farmers dataset, which requires a little more prep to be meaningful:

# Chunk 8
# #1
zamr2 <- raster(x = extent(districts), crs = crs(districts), res = 0.25)
values(zamr2) <- 1:ncell(zamr2)

# #2
farmersr <- farmers %>% distinct(uuid, .keep_all = TRUE) %>% 
  dplyr::select(x, y) %>% mutate(count = 1) %>% 
  st_as_sf(coords = c("x", "y"), crs = 4326) %>% 
  rasterize(x = ., y = zamr2, field = "count", fun = sum) %>% print()
#> class      : RasterLayer 
#> dimensions : 39, 47, 1833  (nrow, ncol, ncell)
#> resolution : 0.25, 0.25  (x, y)
#> extent     : 21.99978, 33.74978, -17.97621, -8.226213  (xmin, xmax, ymin, ymax)
#> crs        : +proj=longlat +datum=WGS84 +no_defs 
#> source     : memory
#> names      : layer 
#> values     : 1, 152  (min, max)

# #3
par(mar = c(0, 0, 1, 4))
districts %>% st_union %>% 
  plot(col = "grey", border = "grey", 
       main = expression(paste("N farmers per 0.25", degree, " cell")))
#> although coordinates are longitude/latitude, st_union assumes that they are planar
plot(farmersr, add = TRUE)

In #1, we create a coarser scale (0.25 degree) version of zamr (zamr2), because we want our final raster how count how many farmers responding to our survey are found in each grid cell. The resolution of 0.1 degrees used for zamr is a bit too fine to convey the information nicely in a plot.

In #2, we do the rasterization as part of a pipeline. The first two lines prepare the farmers dataset. Recall that farmers consists of weekly reporting data sent to us by a large number of farmers, which means that we have multiple reports sent by the same farmer (and thus repeated coordinates for each farmer). So we need to reduce farmers down to just one row for each individual farmer, so that we have just a single set of coordinates for each. We do that by using distinct on the uuid variable, using .keep_all = TRUE so that we retain the coordinates, and add a new count variable (which assigns a value of 1 to each farmer) before converting farmers to sf in the third line. We then rasterize the count variable, using the sum function to aggregate the number of farmers per 0.25\(\circ\) grid cell.

The resulting plot (#3) shows that most cells have less than 20 farmers. We add an extra plot decoration step, using expression with paste to add a superscript degree symbol to our plot title.

You can also rasterize line features, much as we did for points and polygons, but rasterize is exceedingly slow for lines, so we are not doing that here. However, there is code below that shows how one could so that with the roads dataset (subset to roads greater than 100 km long):

# Chunk 9
roadsr <- roads %>% filter(as.numeric(st_length(.)) > 1000000) %>% 
  mutate(ID = 1:nrow(.)) %>% st_transform(crs = 4326) %>% 
  rasterize(., zamr, field = "ID")

2.3.2 Raster to vector

raster gives us functions that allow us to transform rasters to vectors.

# Chunk 10
# #1
dists_fromr <- rasterToPolygons(x = distsr, dissolve = TRUE) %>% st_as_sf

# #2
farmers_fromr <- rasterToPoints(x = farmersr, spatial = TRUE) %>% st_as_sf

par(mar = c(0, 0, 0, 0))
dists_fromr %>% st_geometry %>% plot(col = topo.colors(n = nrow(districts)))
farmers_fromr %>% plot(pch = 20, col = "red", add = TRUE)

Vectorizing rasters and vectorizing back again means that you end up with lower resolution vectors if the raster is fairly coarse. You will note that this has occurred here, both in converting the rasterized districts back to polygons (#1) and the rasterized farmer counts back to points (#2). There are several things to note here. First, we used different functions for vectorizing polygons and points. Second, we piped each vectorization output to st_as_sf, because the endresult of the rasterTo* functions is an sp object, so the extra coerces those to sf.

2.5.1 Questions

1. What is a primary difference between sf and s4 object classes?

2. What function should you use to read and write a multi-layer raster?

3. What are the difference between stack and brick?

4. What class of object do raster’s vectorization functions produce?

2.5.2 Code

1. Create a new raster r4, using r3 (above) as a template. Update the values of r4 using numbers randomly selected from a uniform distribution ranging between 0 and 1. Create another raster r5 by finding the values greater than 0.5 in r4. Recreate the list l with r, r2, r3, r4, and r5, and then create and plot stack s2.

2. Create a new brick b2 by applying the brick function to s2 and writing it out to disk as b2.tif, specifying the path to your notebooks/data folder.

3. Following the steps in Chunk 8, recreate farmersr by re-rasterizing farmers at a 0.2 degree resolution. Plot the result.

4. Project the new 0.2 degree resolution farmersr to an Albers projection with a target resolution of 20 km (20,000 m), calling it farmersr_alb. Chunk 11 is your guide, but reproject using a bilinear rather than nearest neighbor interpolation (see ?projectRaster). Make a two panel plot comparing farmersr on the left, plotted over the unioned districts of Zambia in grey, with farmersr_alb on the right, plotted over the unioned districts of Zambia in grey (and transformed to Albers). Code in Chunks 8 and 11 can help.

5. Convert distsr to an sf polygons object, using rasterToPolygons with dissolve = TRUE. Plot the result without coercing to st_geometry.

3.1.1 Masking

We are interested in the rainfall data within Zambia’s borders, so we need to mask out the values of chirps that fall outside of Zambia:

# Chunk 16
test_m <- mask(x = chirps[[1]], mask = districts)
par(mar = c(0, 0, 0, 4))
plot(test_m, axes = FALSE, box = FALSE)  

In the code above, we use the districts data to mask out the portions of chirps (the first day in the time series only) falling outside of Zambia. Let’s apply that to the entire chirps dataset:

# Chunk 17
chirpsz <- mask(x = chirps, mask = districts)

set.seed(1)
ind <- sample(1:nlayers(chirpsz), size = 3)
plot(chirpsz[[ind]], axes = FALSE, box = FALSE, nr = 1)

The new chirpsz dataset contains all rainfall days with the values outside of Zambia converted to NA. The three plots are randomly selected from the layers of chirpsz, as a check to confirm that the masking was applied to all layers.

3.1.2 Cropping

If we need to chop a raster down to a smaller region, we can crop it. crop uses the extent of another object to achieve this.

# Chunk 18
chirps1_dist72 <- crop(x = chirpsz[[1]], y = districts %>% slice(72))

par(mar = c(0, 0, 0, 2))
chirps1_dist72 %>% plot(axes = FALSE, box = FALSE)
districts %>% st_geometry %>% plot(add = TRUE)
districts %>% st_centroid %>% st_coordinates %>% 
  text(x = ., labels = row.names(.))

The above uses the extent of district 72 (dist72) to crop the first layer of chirpsz. Note that in the plotting step we can pipe the cropped raster to plot, and also that we can label the district numbers on the plot by extracting their centroid coordinates and passing these into the “x” argument of text, and then using the row.names of the piped-in data.frame of centroid coordinates as the labels.

Cropping is important if we want to confine further analyses to a particular sub-region. However, if we just want to focus our plot to a particular region, then we can simply zoom the plot to that region (without cropping) using an extent object.

# Chunk 19
par(mar = c(0, 0, 0, 2))
plot(chirpsz[[1]], axes = FALSE, box = FALSE, ext = extent(districts[72, ]))
districts %>% st_geometry %>% plot(add = TRUE)
districts %>% st_centroid %>% st_coordinates %>% 
  text(x = ., labels = row.names(.))

# Chunk 20
plot_noaxes <- function(x, axes = FALSE, box = FALSE, mar = c(0, 0, 1, 4), 
                        ...) {
  if(!class(x) %in% c("RasterLayer", "RasterStack", "RasterBrick", "Extent")) {
    stop("This function is intended for rasters only", call. = FALSE)
  }
  par(mar = mar)
  plot(x, axes = axes, box = axes, ...)
}

# Chunk 21
plot_noaxes(chirpsz[[1]])

# chirpsz[[1]] %>% plot_noaxes  # also works in a pipeline

3.1.3 Aggregating/disaggregating

To change to resolution of a raster object, you can use aggregate to make a coarser resolution, or disaggregate to decrease the resolution. To make chirpsz match the 0.1 resolution of distsr (the rasterized districts), we do this:

# Chunk 21
chirpsz1agg <- aggregate(x = chirpsz[[1]], fact = 2, fun = mean)
chirpsz1agg
#> class      : RasterLayer 
#> dimensions : 99, 117, 11583  (nrow, ncol, ncell)
#> resolution : 0.1, 0.1  (x, y)
#> extent     : 21.95, 33.65, -18.1, -8.200001  (xmin, xmax, ymin, ymax)
#> crs        : +proj=longlat +datum=WGS84 +no_defs +ellps=WGS84 +towgs84=0,0,0 
#> source     : memory
#> names      : Y16299 
#> values     : 0, 12.18843  (min, max)

We aggregate the first layer of chirpsz by a factor of 2 (fact = 2), taking the average of the aggregated pixels (fun = mean). Since the starting resolution was 0.05, doubling the pixel size takes it to 0.1. We could have chosen to aggregate all layers, and we could have chosen a different aggregation function (e.g. sum, max).

To disaggregate, there are two options:

# Chunk 22
chirpsz1km <- disaggregate(x = chirpsz[[1]], fact = 5)
# chirpsz1km <- disaggregate(x = chirpsz[[1]], fact = 5, method = "bilinear") 
chirpsz1km
#> class      : RasterLayer 
#> dimensions : 985, 1170, 1152450  (nrow, ncol, ncell)
#> resolution : 0.01, 0.01  (x, y)
#> extent     : 21.95, 33.65, -18.05, -8.200001  (xmin, xmax, ymin, ymax)
#> crs        : +proj=longlat +datum=WGS84 +no_defs +ellps=WGS84 +towgs84=0,0,0 
#> source     : memory
#> names      : Y16299 
#> values     : 0, 18.00534  (min, max)

The first option is the default one, which just breaks apart each pixel into the number of smaller new pixels specified by the factor, assigning each new pixel the same value as its larger parent. Here we specified a factor of 5, leading to an output resolution of 0.01 (~1 km), and thus 25 times the number of pixels as in the original chirpsz[[1]] (run ncell(chirpsz1km) / ncell(chirpsz[[1]]) to see).

The second way (commented out), is to set method = bilinear, which interpolates during disaggregation. In this case, disaggregate does the job using the resample function, which we will see next.

3.1.4 Resampling

Resampling is done for many reasons, but one particularly common case is as a final step following aggregation or disaggregation, when it is needed to co-register the resulting grid to another grid.

# Chunk 23
chirps125 <- aggregate(x = chirpsz[[1]], fact = 5)  # no fun b/c default is mean
s <- stack(chirps125, farmersr)  # fails 
#> Error in compareRaster(x): different extent

par(mar = c(1, 1, 1, 1))
plot(extent(chirps125), axes = FALSE, col = "blue")
plot(extent(farmersr), add = TRUE, col = "red")

After aggregating chirpsz layer 1, we try and fail to stack the result with farmersr, because (as the plot of extents show, and the warning tells) the two objects have different extents. So, another approach is needed:

# Chunk 24
farmersr_rs <- resample(x = farmersr, y = chirps125) 
s <- stack(chirps125, farmersr_rs)  
names(s) <- c("rain", "farmer_count")
plot_noaxes(s)

We resample farmersr to chirps125rs, since chirps125rs has the larger extent. However, there is one more thing we should do before using these data, and that is an adjustment to farmersr. Have a look at this:

plot_noaxes(s$farmer_count >= 0)
plot(st_geometry(st_union(districts)), add = TRUE)
#> although coordinates are longitude/latitude, st_union assumes that they are planar

This shows that there are no places where there are 0 farmers–because the original data contributing to farmersr (the second layer in s) was derived from point locations representing the approximate locations of where farmers were interviewed. The data thus have no points where there were 0 farmers interviewed (it would be silly to conduct an interview with no subject), thus everywhere outside of interview locations is assigned a no data value. These are not analyzed in raster operations. So we have to fix this if we want to have the full area of Zambia in the second layer of our stack.

s$farmer_count[is.na(s$farmer_count)] <- 0
s$farmer_count <- mask(s$farmer_count, s$rain)
plot(s$farmer_count)
plot(st_geometry(st_union(districts)), add = TRUE)
#> although coordinates are longitude/latitude, st_union assumes that they are planar

Now all the areas in s$farmer_counts where no interviews were conducted area set to 0.

We can then stack and perform subsequent analyses that draw on both layers, e.g. finding areas where rainfall exceeded 1 mm and where there was more than 1 farmer:

# Chunk 25
plot_noaxes(s$farmer_count > 1 & s$rain > 1)

# (s$rain > 1 & s$farmer_count > 1) %>% plot_noaxes  # also works

3.2.1 Global statistics

The most basic analyses to perform on rasters is to calculate global summary statistics, i.e. statistics calculated across all cell values:

# Chunk 26
cellStats(x = chirpsz[[1]], stat = "mean")  # for a single date
#> [1] 0.6971701
cellStats(x = chirpsz[[c(5, 7, 14)]], stat = "mean")
#>    Y16303    Y16305    Y16312 
#> 0.3895292 0.8927849 0.5229256
summary(chirpsz[[1:3]])
#>              Y16299      Y16300       Y16301
#> Min.        0.00000     0.00000     0.000000
#> 1st Qu.     0.00000     0.00000     0.000000
#> Median      0.00000     0.00000     0.000000
#> 3rd Qu.     0.00000     0.00000     0.000000
#> Max.       18.00534    17.76521     8.853778
#> NA's    20995.00000 20995.00000 20995.000000

cellStats lets you calculate specific statistics from the cell values of a lone RasterLayer, or for a single, multiple, or all layers in a RasterStackBrick. summary (a generic) returns the quintile values and counts the number of NA or no data cells. Both functions by default remove NA values (which are in many if not most rasters), which is something that usually has to be specified when trying to apply these statistical functions to an ordinary vector, e.g. 

# Chunk 27
v <- values(chirpsz[[1]])
mean(v) 
#> [1] NA
mean(v, na.rm = TRUE)
#> [1] 0.6971701

v is a vector of all of the values from the first layer in the rainfall brick, including its NA values. mean returns an NA if you don’t tell the function to remove NA values first. This is important to remember, because both spatial and non-spatial data often have missing values, so you will have to deal with them explicitly in many cases.

Here’s a more programmatic way of using cellStats:

# Chunk 28
# #1
rain_stats <- lapply(list(mean, sum, sd, cv), function(x) {
  cellStats(x = chirpsz, stat = x)
})
names(rain_stats) <- c("mean", "sum", "sd", "cv")

# #2
rain_statsf <- do.call(cbind, rain_stats) %>% data.frame %>% 
  mutate(date = as.Date(gsub("Y", "", row.names(.)), "%y%j"))
# do.call(cbind, rain_stats) %>% data.frame
# do.call(cbind, rain_stats) %>% row.names %>% gsub("Y", "", .)
# do.call(cbind, rain_stats) %>% row.names %>% gsub("Y", "", .) %>%
#   as.Date(., "%y%j")

# #3
ps <- lapply(c("mean", "sum", "sd", "cv"), function(x) { # x <- "mean"
  ggplot(rain_statsf %>% dplyr::select(date, all_of(x))) + 
    geom_line(aes_string("date", x)) + xlab("")
})
cowplot::plot_grid(plotlist = ps)

In #1 we use lapply to calculate 4 different statistics over all dates in chirpsz, meaning that we get a time series for each statistic as calculated over all of Zambia.

In #2, we use a pipeline to bind the summary time series vectors into a data.frame (one statistic per column), and then do some gymnastics to convert the row names of the data.frame, which are constructed from the layer names of chirpsz (which are stored as “Y16XXX”, where XXX is the julian day) to a vector of dates. Work through the commented out code below this line, which breaks down the steps used to create the date variable. gsub first replaces the “Y” in each name, and then as.Date parses the remaining numbers into an actual date. The “%y%j” construction tells as.Date which parts of the character string relate to which part of a date: %y = two digit year; %j = julian day; placed next to one another %y%j means these two elements are immediately adjacent to one another in the string.

We use lapply to set up four ggplot objects in #3 (note the use of aes_string rather than aes, which allows the variable names to be passed as string, rather than unquoted), and then use cowplot::plot_grid to put those plots in a grid, using the “plotlist” argument to receive the input list of ggplots.

The results in the plot above are actually quite interesting. The top two panels show when the rainy season gets underway in earnest (just after Nov 8). The bottom two panels show two measures of variability, the standard deviation (SD) and coefficient of variation (CV, i.e. SD / mean). These two measures summarize the spatial variability of rainfall falling across Zambia on each day–SD increases as the amount of rain increases (which is expected–SD is usually positively correlated with the mean), whereas CV declines as rainfall increases, indicating that a progressively larger area of the country receives rainfall as the month progresses, so there is less spatial variability. There is a big spike in CV on November 8, which corresponds to a drop in mean and total rainfall. However, that drop masks the fact that there are a few small patches that received a decent amount of rainfall, thus leading to a high CV (see next plot below).

# Chunk 29
plot_noaxes(chirpsz[[15]], main = paste("CV =", round(rain_stats$cv[15])))

Another way to summarize raster data is visually, using a histogram (raster has a generic hist function)

# Chunk 30
par(mfrow = c(1, 3))
hist(chirpsz[[15:17]], col = "blue", xlab = "mm")

This variant plots a histogram per layer in the Raster* object (but we told it to plot 1 row, 3 columns, instead of the default (2 rows, 2 columns)).

freq is another way to summarize raster values that is similar to hist but without the automatic plot.

# Chunk 31
f <- freq(chirpsz[[1]]) %>% print()
#>       value count
#>  [1,]     0 21053
#>  [2,]     1   234
#>  [3,]     2   698
#>  [4,]     3   817
#>  [5,]     4   660
#>  [6,]     5   544
#>  [7,]     6   432
#>  [8,]     7   306
#>  [9,]     8   175
#> [10,]     9    59
#> [11,]    10    42
#> [12,]    11    41
#> [13,]    12    27
#> [14,]    13     7
#> [15,]    14     3
#> [16,]    15     2
#> [17,]    16     2
#> [18,]    18     1
#> [19,]    NA 20995

Here we apply freq to a dataset with continuous values, although this function is probably best reserved for categorical rasters. However, it produces reasonable results here.

3.2.2 Local statistics

The previous section showed us how to produce statistics calculated across the entire raster. Now we will learn to calculate local, or neighborhood, statistics.

# Chunk 32
# #1
zonemu <- zonal(x = chirpsz, z = distsr, fun = "mean")  # fails b/c extent
#> Error in compareRaster(c(x, z)): different extent

# #2
distsr_rs <- resample(x = distsr, y = chirpsz, method = "ngb")  # match extent
zonemu <- zonal(x = chirpsz, z = distsr_rs, fun = "mean")
head(zonemu)[, 1:5]
#>      zone     Y16299    Y16300    Y16301    Y16302
#> [1,]    1 0.00000000 0.0000000 0.0000000 1.8976312
#> [2,]    2 0.01322501 0.0000000 0.0000000 0.0000000
#> [3,]    3 6.04584049 1.8021238 0.0000000 4.4494707
#> [4,]    4 0.00000000 0.3011147 0.0201552 0.0000000
#> [5,]    5 6.25742351 3.6532615 1.0868976 0.4739815
#> [6,]    6 0.00000000 0.0000000 0.0000000 0.0000000

# Chunk 33
distr_rfmu <- zonemu %>% data.frame %>% dplyr::select(1:2) %>% 
  subs(x = distsr_rs, y = ., by = "zone")
plot_noaxes(distr_rfmu)

# Chunk 34
# #1
wmat <- matrix(1 / 9, nrow = 3, ncol = 3) 
chirps1_focmu1 <- focal(x = chirpsz[[1]], w = wmat) 

# #2
wmat <- matrix(1, nrow = 3, ncol = 3) 
chirps1_focmu2 <- focal(x = chirpsz[[1]], w = wmat, fun = mean) 

# #3
wmat <- matrix(1, nrow = 5, ncol = 5) 
chirps1_focmu3 <- focal(x = chirpsz[[1]], w = wmat, fun = mean) 

# #4 
wmat <- matrix(1, nrow = 5, ncol = 5) 
chirps1_focmu4 <- focal(x = chirpsz[[1]], w = wmat, fun = mean, na.rm = TRUE) 

# #5
wmat <- matrix(1 / 9, nrow = 5, ncol = 5) 
chirps1_focmu5 <- focal(x = chirpsz[[1]], w = wmat, na.rm = TRUE) 

# plots
l <- list(chirps1_focmu1, chirps1_focmu3, chirps1_focmu4, chirps1_focmu5)
titles <- c("3X3 NAs not removed", "5X5 NAs not removed", 
            "5X5 NAs removed properly", "5X5 NAs removed improperly")
par(mfrow = c(2, 2))
for(i in 1:length(l)) {
  plot_noaxes(l[[i]], main = titles[i])
}

3.2.3 Analyzing the Z dimension

If we have a RasterStackBrick, we have three dimensions (x, y, z). Often we want to analyze the values in the Z dimension (which may represent time, spectral bands, or unrelated spatial predictors in a model) without altering the x and y dimensions.

The workhorse for doing this sort of analysis is calc, which allows you to apply pretty much any function to the Z-dimension of a RasterStackBrick.

# Chunk 35
# #1
rain_zmu <- calc(x = chirpsz, fun = mean)
rain_zsd <- calc(x = chirpsz, fun = sd)
rain_zrng <- calc(x = chirpsz, fun = range)

# #2
rain_zstack <- stack(rain_zmu, rain_zsd, rain_zrng)
names(rain_zstack) <- c("Mean", "StDev", "Min", "Max")

plot_noaxes(rain_zstack)

In #1 we pass mean, sd, and range to “fun” in calc. Note that range always returns two values, so calc conveniently returns a two-layer brick that contains the minimum in the first layer and the maximum in the second.

In #2 we then stack the three outputs, and rename the layers something meaningful so that plot_noaxes can plot them all at once.

You will see from the resulting plot that “Min” has only one value, 0, which makes sense for a rainfall time series (every pixel is likely to have at least one day of no rainfall over the course of a month).

3.3.1 Questions

1. How do cellStats, focal, and zonal differ from one another?

2. How do you disaggregate a raster with interpolation?

3. How do you run calc on images with different resolutions or extents?

3.3.2 Code

1. Run as.Date("10-11-2017", "%m-%d-%Y"), as.Date("10-11-17", "%m-%d-%y"), as.Date("101117", "%m%d%y"), and as.Date("10112017", "%m%d%Y") to get a better sense of date vectors work. Also try out lubridate::mdy("10-11-2017") and lubridate::as_date("20171011").

2. Convert farmers to a 0.1 degree raster (farmersr2) that contains the count of farmers per grid cell. Use distsr as the target raster so that the extents align.

3. Use zonal on farmersr2 to calculate the total number of farmers per district (use distsr to provide the zones), and then map them back onto the districts/zones using subs. Plot the result.

4. Use focal to calculate for chirpsz[[20]] the i) standard deviation within a 3X3 and 5X5 window, and ii) the maximum value in each 3X3 and 5X5 neighborhood. Do not remove NAs. Combine the results in a stack, as above, and then plot them using plot_noaxes.

5. Crop chirpsz[[1]] using the extent of districts[57, ], and disaggregate it to 0.01 resolution using both the default and bilinear methods. Plot the results side by side using plot_noaxes.

6. Use calc with chirpsz to calculate the total rainfall in the time series, the coefficient of variation, and the median. Stack the results and plot with meaningful titles using plot_noaxes (hint: name the layers of the stack), outputting plots on 1 row with 3 columns.

4.3.1 Extract

From the description of extract, the function’s purpose is to:

Extract values from a Raster* object at the locations of other spatial data. You can use coordinates (points), lines, polygons or an Extent (rectangle) object. You can also use cell numbers to extract values.

Here we will use points and polygons:

# Chunk 40
# #1
farmers_env <- farmers %>% distinct(uuid, .keep_all = TRUE) %>% 
  dplyr::select(uuid, x, y) %>% st_as_sf(coords = c("x", "y")) %>% 
  mutate(rain = raster::extract(x = raintot, y = .)) %>%
  mutate(district = raster::extract(x = distsr_rs, y = .)) %>% print
#> Simple feature collection with 793 features and 3 fields
#> geometry type:  POINT
#> dimension:      XY
#> bbox:           xmin: 24.777 ymin: -18.222 xmax: 33.332 ymax: -8.997
#> CRS:            NA
#> # A tibble: 793 x 4
#>    uuid             geometry  rain district
#>  * <chr>             <POINT> <dbl>    <dbl>
#>  1 009a8424 (27.256 -16.926)  66.9       11
#>  2 00df166f (26.942 -16.504)  72.0       11
#>  3 02671a00 (27.254 -16.914)  66.9       11
#>  4 03f4dcca (27.237 -16.733)  69.8       11
#>  5 042cf7b3 (27.138 -16.807)  75.1       11
#>  6 05618404 (26.875 -16.611)  66.1       11
#>  7 064beba0 (26.752 -16.862)  58.4       20
#>  8 083a46a2 (26.977 -16.765)  70.4       11
#>  9 08eb2224 (26.912 -16.248)  54.0       59
#> 10 0ab761d6  (27.113 -16.95)  72.4       11
#> # … with 783 more rows

# #2
farmdistid <- farmers_env %>% drop_na %>% distinct(district) %>% pull
distrain <- districts %>% filter(ID %in% farmdistid) %>% 
  raster::extract(x = raintot, y = ., fun = mean) %>% print
#>           [,1]
#>  [1,] 58.35027
#>  [2,] 36.46143
#>  [3,] 67.99078
#>  [4,] 45.12769
#>  [5,] 44.12176
#>  [6,] 69.70491
#>  [7,] 41.09122
#>  [8,] 44.15476
#>  [9,] 54.94505
#> [10,] 63.98032
#> [11,] 52.09214
#> [12,] 49.01939
#> [13,] 51.98236
#> [14,] 46.55391
#> [15,] 61.68815
#> [16,] 53.98820
#> [17,] 60.90310

# #3
rain_stats <- bind_rows(
  farmers_env %>% drop_na %>% dplyr::select(rain) %>% mutate(dat = "Farmers"), 
  tibble(rain = distrain, dat = "Districts")
)

# #4
bp_theme <- theme(legend.title = element_blank(), axis.text.x = element_blank(),
                  axis.ticks.x = element_blank(), 
                  panel.grid.major.x = element_blank(), 
                  panel.grid.minor.x = element_blank(), 
                  panel.background = element_rect(fill = "grey95"))
rain_stats %>% ggplot() +
  geom_boxplot(mapping = aes(y = rain, fill = dat), position = "dodge2") +
  scale_fill_manual(values = c("steelblue", "cadetblue")) + 
  ggtitle("Rainfall distributions") + xlab(NULL) + ylab("mm") + bp_theme

In #1, we use a pipeline to create a new farmer_env sf (first selecting just the unique uuid and corresponding x and y), and we pass that to the “y” argument of raster::extract. The first extract is done from the raintot raster, the second from the dists_rs raster. Both extractions are wrapped in mutate, in order to create two new variables for farmers_env. Note that we have to specify raster::extract because it is masked by dplyr::extract, as geospaar loads tidyverse after raster (remember section 1.2.2 in Unit 1 Module 2). The resulting sf contains rainfall sum (over the 28 days) and district numbers for each farmer’s location.

In #2, we first pull out of farmer_env a vector of the distinct district IDs. Because farmers contains a few bad coordinates that fall outside of Zambia, and there had NA values, we inserted drop_na into the pipeline to get rid of those. We then used farmdistid to filter out the districts the farmers live in from districts, and used the result to extract from raintot the mean rainfall from the pixels of raintot falling within each selected district. When using raster::extract with polygons, if you don’t pass a value to the “fun” argument, a list is returned, in which each element contains the extracted pixel values corresponding to a particular polyon. If you give “fun” an argument (e.g. mean, as in this case), you get back a vector or matrix (if your function gives back more than one value, e.g. range) containing the resulting statistic(s) for each polygon.

In #3, we do some gymnastics in preparation for setting up ggplot boxplots (#4) that compare the distributions of rainfall values. That is, we set up a tibble that binds by row the extracted district and farmer rainfall values, which allows ggplot to automatically create side-by-side boxplots using fill = dat. We create some theme options for ggplot ahead of that bp_theme, so that we can recycle these in the next example. The plot shows that the rainfall data selected at farmer locations provide a biased estimate of district mean rainfall.

4.3.2 Random sampling

Alternatively, you might want to draw a random sample directly from a raster, without all the trials and tribulations of field work (field logistics often make it hard to capture truly randomized, and thus representative, samples). raster has functions for this, and we will build off the previous example to demonstrate them.

# Chunk 41
# #1
farmdistsr <- distsr_rs %in% farmdistid
distsrfarm <- mask(x = distsr_rs, mask = farmdistsr, maskvalue = 0)
# plot_noaxes(distsrfarm)

# #2
set.seed(1)
distsamp <- sampleRandom(x = distsrfarm, size = nrow(farmers_env), cells = TRUE)
randrain <- raintot[distsamp[, 1]]

# #3
set.seed(1)
distsamp_str <- sampleStratified(x = distsrfarm, 
                                 size = nrow(farmers_env) / length(farmdistid),                                  cells = TRUE)
stratrandrain <- raintot[distsamp_str[, 1]]

# #4
rand_rain_stats <- bind_rows(
  tibble(rain = distrain, dat = "Districts"),
  tibble(rain = randrain, dat = "Simple"),
  tibble(rain = stratrandrain, dat = "Stratified")
) %>% drop_na

rand_rain_stats %>% ggplot() +
  geom_boxplot(mapping = aes(y = rain, fill = dat), position = "dodge2") +
  scale_fill_manual(values = c("lightblue", "steelblue", "cadetblue")) + 
  ggtitle("Rainfall distributions") + xlab(NULL) + ylab("mm") + bp_theme

In this case, we first (#1) mask the raster to exclude districts having no farmers (you can run the commented-out code to see the map). #2 uses the function raster::sampleRandom to take a straight random sample from the farmer-hosting districts. We set the “size” argument so that it is equal to nrow(farmers_env), i.e. our sample is equal to the number of farmers in farmers_env (793). We use the argument cells = TRUE to select the cell numbers, which is what we are really interested in (if we didn’t, we would just get the values of those cells, i.e. the district IDs). We then use those cell ids (the first column of distsamp) to extract the rainfall values from raintot. We can use the cell IDs selected from one raster to extract values from another only if the two rasters have an identical number of cells and extents, as is the case here. You can confirm that this is the case for distsrfarm and raintot by running identical(ncell(raintot), ncell(distsrfarm)) and identical(extent(raintot), extent(distsrfarm)).

In #3 we apply the more correct way of collecting a representative sample from units of varying size, which is to stratify the sample by districts. To do this, we uses the function sampleStratified, which uses the district IDs in distsrfarm to create the strata, and the “size” argument specifies the size of the sample that should be drawn from each stratum (i.e. district). To estimate that size, we divide nrow(farmers_env) by the number of farmer-hosting districts, so that we end up with a total sample equal to 793. Note that this function merely ensures that the same sample size is drawn from each stratum (district), and does not make the sample size in each stratum proportional to its area.

In #4, we redo the boxplots, showing the results from the two approaches to random sampling alongside the distribution of district mean rainfall values (extracted in Chunk 40). Both approaches produce statistics that are quite representative of the district rainfall. The stratified approach is closest, as the median aligns more closely with that of distrain.

4.4.1 Questions

1. What are two ways of converting a continuous to categorical raster?

2. What are two methods of sampling from a raster? Are the others (a look in rasters help files will be informative)?

4.4.2 Code

1. Use calc to find the standard deviation of rainfall for each cell in chirpsz.

2. Use raster algebra to find the country-wide average standard deviation, and then identify which areas of Zambia have values less than that.

3. Create a new categorical raster from raintot, using the quantile to define the new category boundaries together with cut. Use plot_noaxes to show the result.

4. Create a new sub-sample of rasterized districts, randdistsr, totaling 15 districts randomly selected using dplyr::sample_n (use a seed of 11) from districts. Use raintot as the rasterization target. Mask raintot so that it is confined to those districts (with NAs values replacing the values in the other districts). Call it newrandrain.

5. Use sampleRandom with a size of 300 to get a random sample of rainfall values from newrandrain (use a seed of 1), saving the result as randsamp. Use sampleStratified with cell = TRUE to get a sample of 300 / 15 samples from randdistsr. Use the cell IDs to extract the rainfall values from newrandrain, saving the output vector as stratsamp. Create a tibble that binds these two vectors by row (as in Chunk 41 #4), and then plot the two results as side-by-side boxplots with ggplot.

5.1.1 Pixel resolution/area

The DEM we downloaded is in decimal degrees with a resolution of 0.0083333°, which means the area of each pixel varies through Zambia. To illustrate that, we use a nice function that raster provides, which lets you calculate the pixel areas, even when the raster is in geographic coordinates:

# Chunk 43
demarea <- area(dem)
plot_noaxes(demarea, legend.args = list(text = expression("km"^2)), 
            main = paste("DEM pixel area, mean = ", 
                         round(cellStats(demarea, mean), 3)))
districts %>% st_geometry %>% plot(add = TRUE)

The result is in km\(^2\), and you can see that the area of each pixel falls as the distance from the equator increases (this is why we use equal area projections to calculate area).

5.1.2 An aside on plot annotation

Although we covered graphics in the previous unit, let’s look a bit more at plot adornments for a second. Notice in the last two plots how we use the “legend.args” argument in plot_noaxes to put a title over the legend bar. And in the last one, we use expression to turn km2 into km\(^2\). expression and several other functions can be used to annotate plots with more complex mathematical expressions:

# Chunk 44
set.seed(1)
a <- sapply(20:100, function(x) rnorm(n = 100, mean = x, sd = x / 10))
mu <- colMeans(a)  # means
mumu <- round(mean(mu), 2) # mean of mean
sdev <- apply(a, 2, sd)  # stdevs
musd <- round(mean(sdev), 2)  # mean of stdevs
plot(mu, sdev, xlab = expression(mu), ylab = expression(sigma), pch = 20, 
     main = expression(paste("Mean (", mu, ") versus StDev (", sigma, ")")))
text(x = 20, y = 10, pos = 4,
     label = substitute(paste("Overall ", mu, "=", a), list(a = mumu)))
text(x = 20, y = 9, pos = 4,
     label = substitute(paste("Overall ", sigma, "=", a), list(a = musd)))

The example above shows how more advanced plot annotations can be done. It also shows that the code can get somewhat complicated; it always takes a ton of time and a number of internet searches to figure out how to do this. We won’t explain this in detail here, but the code provides a template that you can hack at if you want to get fancy with labelling your plots.

5.1.3 Basic terrain variables

raster::terrain allows us to calculate five different terrain variables, four of which we show below:

# Chunk 45
# #1
zamr <- raster(x = extent(districts), crs = crs(districts), res = res(dem))
values(zamr) <- 1:ncell(zamr)
zamr_alb <- projectRaster(from = zamr, res = 1000, crs = crs(roads), 
                          method = "ngb")
demalb <- projectRaster(from = dem, to = zamr_alb)  # default is bilinear

# #2
# slope <- terrain(x = demalb, opt = 'slope', unit = 'degrees')  # slope
# aspect <- terrain(x = demalb, opt = 'aspect', unit = 'degrees')  # aspect
# flowdir <- terrain(x = demalb, opt = 'flowdir')  # flow direction
# tri <- terrain(x = demalb, opt = 'tri')  # topographic roughness index
vars <- c("slope", "aspect", "flowdir", "tri")
terrvars <- stack(lapply(1:length(vars), function(x) {
  tv <- terrain(x = demalb, opt = vars[x], unit = "degrees")
}))
names(terrvars) <- vars

plot_noaxes(terrvars)

We need the DEM in a projected coordinate system for terrain to work, per the help file:

Compute slope, aspect and other terrain characteristics from a raster with elevation data. The elevation data should be in map units (typically meter) for projected (planar) raster data. They should be in meters when the coordinate reference system (CRS) is longitude/latitude.

So we create (#1) a 1 km projected version of the DEM, allowing the default bilinear interpolation to do its work during reprojection.

In #2 we calculate slope, aspect, flow direction, and the topographic ruggedness index. The commented out code illustrates how each of these variables can be calculated separately, although we prefer to do the job using lapply. Note that in the lapply we pass the “unit” argument into the calculation of all four variables, even though it only is used for slope and aspect; this is fine, because terrain simply ignores the argument value in calculating flow direction or TRI.

5.5.1 Questions

1. How do we estimate the pixel area of rasters when they are in non-projected coordinate systems?

2. How can you add mathematical symbols and other special characters (e.g. superscripts) to graphics?

3. When you want to apply a fitted model to a stack or brick of rasters (e.g. pred_stack that provide the model predictor layers, what do we have to remember to do with names(pred_stack)?

5.5.2 Code

1. Crop demalb down to the extent of district 42 (bear in mind that districts needs to be in the same projection as demalb, so transform it first). Then calculate slope, aspect, and TPI on the cropped DEM. Plot the results so that they appear in 3 side by side panels.

2. Using the code in Chunk 46 blocks #1-#3 as your template, re-create IDW interpolations using the original 1000 randomly sampled points. Then create two new ones based on 1) 500 and 2) 250 randomly selected points (use the same seed). Stacking the results in this order: raintotalb, the 1000 point IDW, the 500 point IDW, and the 250 IDW. Plot these in a single call to plot_noaxes, setting zlim = c(0, 150) and passing informative titles to the “main” argument (e.g. “CHIRPS”, “1000 pt IDW”, “500 pt IDW”, etc). There are two ways of doing this: i) the hard way, by copying, pasting, and changing code blocks #2 and #3 for each version of the IDW; ii) the programmatic way, by creating the three IDWs in an lapply. Note: if you choose the elegant way, to make the stack, you will either need to stack(c(raintotalb, idw_list)) or stack(raintotalb, stack(idw_list)) stack the list of three idws, and then stack that with raintotalb.

3. Select (filter) districts 15, 20, 25, 30, 35, 40, 45, and 50 out of districts. Convert the resulting subset of districts to Albers projection, and then extract the centroids of those districts. Convert the centroids to an sp object using as_Spatial. Using raintotalb as your target, use distance or distanceFromPoints to calculate the distances from any point in Zambia to the centroids of those selected districts. Mask the result (you can use raintotalb again for the mask target) and plot it using plot_noaxes.

4. Redo the code in Chunk 49, but use a new random draw of just 25 points to collect the predictors (ref. #2). How much more poorly does this model do than the one with denser observations?